Description of fast matrix multiplication algorithm: ⟨14×18×32:4669⟩

Algorithm type

23 X^{8} Y^{8} Z^{8} + 2 X^{8} Y^{8} Z^{6} + 8 X^{6} Y^{8} Z^{8} + 32 X^{4} Y^{12} Z^{6} + 12 X^{8} Y^{6} Z^{6} + 2 X^{8} Y^{4} Z^{8} + 3 X^{6} Y^{8} Z^{6} + 48 X^{2} Y^{12} Z^{6} + 4 X^{6} Y^{6} Z^{6} + 69 X^{4} Y^{8} Z^{4} + 48 X^{4} Y^{6} Z^{6} + 28 X^{4} Y^{4} Z^{8} + 5 X^{2} Y^{12} Z^{2} + 2 X^{4} Y^{8} Z^{2} + 20 X^{4} Y^{6} Z^{4} + 12 X^{4} Y^{4} Z^{6} + 4 X^{4} Y^{2} Z^{8} + 8 X^{2} Y^{8} Z^{4} + 72 X^{2} Y^{6} Z^{6} + 6 X^{2} Y^{4} Z^{8} + 4 X^{6} Y^{4} Z^{2} + 4 X^{4} Y^{6} Z^{2} + 184 X^{4} Y^{4} Z^{4} + 4 X^{4} Y^{2} Z^{6} + 31 X^{2} Y^{8} Z^{2} + 4 X^{2} Y^{4} Z^{6} + 12 X^{4} Y^{4} Z^{3} + 48 X^{3} Y^{4} Z^{4} + 192 X^{2} Y^{6} Z^{3} + 6 X^{6} Y^{2} Z^{2} + X^{4} Y^{4} Z^{2} + 72 X^{4} Y^{3} Z^{3} + 16 X^{4} Y^{2} Z^{4} + 18 X^{3} Y^{4} Z^{3} + 14 X^{2} Y^{6} Z^{2} + 47 X^{2} Y^{4} Z^{4} + 4 X^{2} Y^{2} Z^{6} + 288 X Y^{6} Z^{3} + 24 X^{3} Y^{3} Z^{3} + 2 X^{4} Y^{2} Z^{2} + 448 X^{2} Y^{4} Z^{2} + 288 X^{2} Y^{3} Z^{3} + 216 X^{2} Y^{2} Z^{4} + 30 X Y^{6} Z + 12 X^{2} Y^{4} Z + 120 X^{2} Y^{3} Z^{2} + 72 X^{2} Y^{2} Z^{3} + 24 X^{2} Y Z^{4} + 48 X Y^{4} Z^{2} + 432 X Y^{3} Z^{3} + 36 X Y^{2} Z^{4} + 24 X^{3} Y^{2} Z + 24 X^{2} Y^{3} Z + 282 X^{2} Y^{2} Z^{2} + 24 X^{2} Y Z^{3} + 186 X Y^{4} Z + 24 X Y^{2} Z^{3} + 36 X^{3} Y Z + 6 X^{2} Y^{2} Z + 24 X^{2} Y Z^{2} + 84 X Y^{3} Z + 282 X Y^{2} Z^{2} + 24 X Y Z^{3} + 12 X^{2} Y Z + 204 X Y^{2} Z + 288 X Y Z^{2} + 36 X Y Z

Algorithm definition

The algorithm ⟨14×18×32:4669⟩ is the (Kronecker) tensor product of ⟨2×2×2:7⟩ with ⟨7×9×16:667⟩.

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.

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